Scaling-based Robust Empirical Modeling of Stream Temperature Across USA

Stream temperature controls the biophysical processes occurring in the aquatic environment. Stream temperature typically follows a diurnal pattern due to the variation in climatic drivers (e.g., solar radiation, air temperature). Existing models need hydrologic and/or climatic variables data to predict stream temperature. Additionally, these models are site-specific, which hinders a robust prediction of fine resolution (e.g., hourly) stream temperature. In light of these limitations, a scaling-based empirical model was developed to predict the diurnal cycle of stream temperature using a corresponding single reference observation as the scaling parameter. Scaling transformed different diurnal cycles into a common dimensionless diurnal cycle, representing different days and stream sites. An extended stochastic harmonic algorithm (ESHA) was then used to parameterize the dimensionless diurnal cycle by utilizing the hourly observations of stream temperature over the growing season (May-October) for 66 monitoring sites across the contiguous U.S. The study sites incorporated a considerable gradient in climate (e.g., temperate, tropical), land use (e.g., agriculture, wetland, developed, vegetation), and hydrology (e.g., slope, characteristic length, drainage area). The model parameters were spatiotemporally robust, which was further investigated by quantifying the sensitivity and uncertainty measures. The model can predict the entire diurnal cycle of hourly stream temperature from one or a set of site- and day-specific reference observation(s). The model can help dynamically assess the stream water quality and ecosystem health.